Wishful Thinking in Strategic Environments

Towards developing a theory of systematic biases about strategies, I analyse strategic implications of a particular bias: wishful thinking about the strategies. I identify a player as a wishful thinker if she hopes to enjoy the highest pay-off that is consistent with her information about the others' strategies. I develop a straightforward elimination process that characterizes the strategy profiles that are consistent with wishful thinking, mutual knowledge of wishful thinking, and so on. Every pure-strategy Nash equilibrium is consistent with common knowledge of wishful thinking. For generic two-person games, I further show that the pure Nash equilibrium strategies are the only strategies that are consistent with common knowledge of wishful thinking. My analysis also illustrates how one can characterize the strategic implications of general decision rules using the tools of game theory.